Solution
= Solution
The roots are $r=(-\gamma\pm\sqrt{\gamma^2-4\omega^2})/2$. They give oscillatory decay for $\gamma\lt 2\omega$, two exponential decays for $\gamma\gt 2\omega$, and $(A+Bt)e^{-\gamma t/2}$ at equality. All tend to zero.
= Solution
The roots are $r=(-\gamma\pm\sqrt{\gamma^2-4\omega^2})/2$. They give oscillatory decay for $\gamma\lt 2\omega$, two exponential decays for $\gamma\gt 2\omega$, and $(A+Bt)e^{-\gamma t/2}$ at equality. All tend to zero.